Deformation of stream surfaces in steady axisymmetric flow

Stream surfaces are used to examine the arrangement of neighboring streamlines in steady, divergence-free axisymmetric flow. Expressions are obtained that relate the angle of intersection between stream surfaces with general orientations to the Stokes stream function and to the specific discharge vector. These expressions are used to quantify deformation to the geometry of streamlines and stream surfaces occurring in axisymmetric flow. The Stokes stream function is presented for an isolated inhomogeneity in hydraulic conductivity with spheroidal geometry. It is shown that axisymmetric flow generated by inhomogeneity rearranges the relative position of a streamline with respect to neighboring streamlines only locally. In contrast, a persistent rearrangement in the orientation and spacing of neighboring streamlines is observed between Large distances upgradient and downgradient from groundwater withdrawal. This characterizes all possible rearrangement of neighboring streamlines in axisymmetric flow; withdrawal (or production) is required for a persistent rearrangement to occur.